# Horizontal Lines

Answer the following questions given the line graphed below.

1. Explain why the line graphed above represents a linear relationship.
2. Create a table containing all the defined ordered pairs shown in the graph.
3. What do you notice about all the $$y$$-values in the table?
4. What is the slope of this line? What method did you use to calculate the slope?
5. What is the $$y$$-intercept of this line? Name this point as an ordered pair.
6. What equation could be used to represent any point on this line?
7. Is this equation in the slope-intercept form?

Horizontal lines have slopes that are in the form $$\dfrac{rise}{run}=\dfrac{0}{a}=0$$, where $$a$$ is an element of the complex numbers.

All horizontal lines have a slope of zero and thus, equations (written in slope-intercept form) are in the form $$y=0x+b$$, which is the same as $$y=b$$.

In the graph shown above, $$b=3$$ and all points have the $$y$$-value of $$3$$ for any value of $$x$$.  In this example, the equation for this horizontal line is $$y=3$$.